LEAPS-MPS: Photonic Topological Edge States on Sharply Joined or Truncated Materials

Depaul University, Chicago IL

Investigators

Abstract

Topological insulators, first discovered in the context of electronics, are materials whose interiors behave like insulators and whose surfaces behave like conductors—that is, waves can travel on the surface but not in the bulk. The surface waves in topological insulators, also known as edge states, are remarkably robust against environmental disturbances and manufacturing defects, making them valuable for transmitting information and energy. Photonic topological insulators are topological insulators for electromagnetic waves, which can be used to make compact and efficient on-chip devices for communication and data processing, and are also utilized in optical isolators, topological lasers, uncompressed video, and ultra-thin electrical shielding components. Photonic topological insulators with sharp interfaces and edges are easy to manufacture, but they have not been addressed in current models in many important contexts. This project investigates photonic topological insulators involving sharp interfaces and edges, which will guide the design and simplify the manufacturing process for photonic devices. This project also provides abundant opportunities for student learning, training, and research. This project aims to show the existence and characterize the behavior of the edge states in photonic topological insulators involving sharp interfaces or edges, within the framework of partial differential equations. The specific objectives include: (1) Identifying edge states on sharp interfaces formed by materials with various symmetries. These geometries arise from settings including the photonic quantum Hall effect, the photonic quantum spin Hall effect, and photonic topological insulators based on square lattices. (2) Identifying edge states on sharply truncated edges, with various truncation locations and boundary conditions. (3) Providing a family of materials satisfying the no-fold assumption, which is a condition for edge states to emerge when certain spectral degeneracies are weakly perturbed. This project will provide theoretical foundations for various types of photonic topological insulators, and will entail an advancement of the mathematical tools of layer potentials and their subtle asymptotic analysis. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.